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<a NAME="E1:7_1_1"/>
( the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <a href="metric_1.html#G1" title="METRIC_1:aggr.1">MetrStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="normsp_2.html#K1" title="NORMSP_2:func.1">distance_by_norm_of</a> <font color="Maroon" title="c1">X</font></span>)</span> #) is <a href="metric_1.html#V2" title="METRIC_1:attr.2">Reflexive</a> &amp; the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <a href="metric_1.html#G1" title="METRIC_1:aggr.1">MetrStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="normsp_2.html#K1" title="NORMSP_2:func.1">distance_by_norm_of</a> <font color="Maroon" title="c1">X</font></span>)</span> #) is <a href="metric_1.html#V3" title="METRIC_1:attr.3">discerning</a> &amp; the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <a href="metric_1.html#G1" title="METRIC_1:aggr.1">MetrStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="normsp_2.html#K1" title="NORMSP_2:func.1">distance_by_norm_of</a> <font color="Maroon" title="c1">X</font></span>)</span> #) is <a href="metric_1.html#V4" title="METRIC_1:attr.4">symmetric</a> &amp; the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <a href="metric_1.html#G1" title="METRIC_1:aggr.1">MetrStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="normsp_2.html#K1" title="NORMSP_2:func.1">distance_by_norm_of</a> <font color="Maroon" title="c1">X</font></span>)</span> #) is <a href="metric_1.html#V5" title="METRIC_1:attr.5">triangle</a> )
 
<b>by </b><i><a class="txt" href="normsp_2.html#E3"><i><font color="Green" title="E2">Lm1</font></i></a>, <a class="txt" href="normsp_2.html#E4"><i><font color="Green" title="E3">Lm2</font></i></a>, <a class="txt" href="normsp_2.html#E5"><i><font color="Green" title="E4">Lm3</font></i></a>, <a class="txt" href="normsp_2.html#E6"><i><font color="Green" title="E5">Lm4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:7_1_1"/>
 <a href="metric_1.html#G1" title="METRIC_1:aggr.1">MetrStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="normsp_2.html#K1" title="NORMSP_2:func.1">distance_by_norm_of</a> <font color="Maroon" title="c1">X</font></span>)</span> #) is  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="metric_1.html#NM1" title="METRIC_1:NM.1">MetrSpace</a>
 <b>by </b><i><a class="ref" href="metric_1.html#D7" title="METRIC_1:def.7">METRIC_1:def 7</a>, <a class="ref" href="metric_1.html#D8" title="METRIC_1:def.8">METRIC_1:def 8</a>, <a class="ref" href="metric_1.html#D9" title="METRIC_1:def.9">METRIC_1:def 9</a>, <a class="ref" href="metric_1.html#D10" title="METRIC_1:def.10">METRIC_1:def 10</a>, <a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>;<br/>


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